Subgroups — #44566697

Order 32192.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632870	C₂	1	1	yes	maximal, characteristic
2	#30632804	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632803	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₅₀₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×C₅₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#22548883	C₄	1	1	yes	characteristic
7	#22548867	C₄	1	1	yes	characteristic
8	#22548866	C₄	1	2	yes	—
9	C₈×D₅₀₃	C₂²	1	2	yes	—
10	C₅₀₃⋊C₁₆	C₂²	1	2	yes	—
11	C₂×C₈×C₅₀₃	C₂²	1	1	yes	characteristic
12	C₁₆×C₅₀₃	C₂²	1	1	yes	characteristic
13	C₁₆×C₅₀₃	C₂²	1	1	yes	characteristic
14	Dic₁₀₀₆	C₈	1	1	yes	characteristic
15	D₂₀₁₂	C₈	1	1	yes	characteristic
16	C₂²⋊D₅₀₃	C₈	1	2	yes	—
17	C₄×D₅₀₃	C₂×C₄	1	2	yes	—
18	C₅₀₃⋊C₈	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
20	C₈×C₅₀₃	C₂×C₄	1	1	yes	characteristic
21	C₈×C₅₀₃	C₂³	1	1	yes	characteristic
22	C₂²×C₅₀₃	C₂×C₈	1	1	yes	characteristic
23	C₂×D₅₀₃	C₂×C₈	1	2	yes	—
24	C₄×C₅₀₃	C₂×C₈	1	1	yes	characteristic
25	C₄×C₅₀₃	C₂²×C₄	1	1	yes	characteristic
26	Dic₅₀₃	C₂×C₈	1	2	yes	—
27	C₂×C₅₀₃	—	2	1	no	—
28	C₂×C₅₀₃	C₂²×C₈	1	1	yes	characteristic
29	D₅₀₃	—	2	2	no	—
30	C₅₀₃	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	503	1	no	maximal, Sylow
32	#131	—	503	1	no	—
33	M₃₂	—	503	1	no	—
34	M₃₂	—	503	2	no	—
35	C₂×C₁₆	—	503	2	no	—
36	C₂×C₁₆	D₅₀₃	1	1	yes	characteristic, complemented
37	#41	—	503	1	no	—
38	M₁₆	—	503	1	no	—
39	M₁₆	—	503	2	no	—
40	C₂×C₈	—	503	2	no	—
41	C₂×C₈	C₂×D₅₀₃	1	1	yes	characteristic
42	C₁₆	—	503	2	no	—
43	C₁₆	C₂×D₅₀₃	1	1	yes	characteristic
44	C₁₆	C₂×D₅₀₃	1	1	yes	characteristic
45	Q₈	—	503	1	no	—
46	D₄	—	503	2	no	—
47	D₄	—	503	1	no	—
48	C₂×C₄	—	503	2	no	—
49	C₂×C₄	C₄×D₅₀₃	1	1	yes	characteristic
50	C₈	—	503	2	no	—
51	C₈	C₄×D₅₀₃	1	1	yes	characteristic
52	C₈	C₂²×D₅₀₃	1	1	yes	characteristic
53	C₂²	—	503	2	no	—
54	C₂²	C₈×D₅₀₃	1	1	yes	characteristic
55	C₄	—	503	2	no	—
56	C₄	C₈×D₅₀₃	1	1	yes	characteristic
57	C₄	C₂×C₄×D₅₀₃	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	1006	2	no	—
60	C₂	C₂×C₈×D₅₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×D₅₀₃
commutator, socle	C₂×C₅₀₃	C₂²×C₈
Frattini	C₈	C₂²×D₅₀₃
Fitting	C₂×C₁₆×C₅₀₃	C₂
prime radical	#22548883	C₄
cosocle	C₈×C₅₀₃	C₂³
hypercenter	C₂×C₁₆	D₅₀₃
hypocenter	C₅₀₃	#504
LCS	G ▷ C₂×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #30632804	C₂	semidirect
3. #30632803	C₂	semidirect
4. C₁₆×D₅₀₃	C₂	semidirect
5. C₂×C₁₆×C₅₀₃	C₂	semidirect
30. C₅₀₃	#504	semidirect
36. C₂×C₁₆	D₅₀₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#30632870	2
#30632804	2
#30632803	2
C₁₆×D₅₀₃	2
C₂×C₁₆×C₅₀₃	2
#504	503